You are absolutely reasonable to be worried. We live in a culture where kids are snacking 24-7 and can't seem to make it from one meal to the other without shoving high-calorie, low nutrient crap in their mouths. I see it all around me and it's genuinely heartbreaking because these kids are not going to grow into healthy adults.
I appreciate that some people think that not allowing snacking/junk/etc is a way to making a kid rebel and want to get it in secret but people rarely apply the same logical fallacy to other behaviours associated with poor health (smoking, drinking, etc).
Obesity has overtaken smoking as the number one cause of some cancers. It is not a joke.
In truth, it's not about making things "forbidden" and "restrictive", but about educating her and fostering a sense of self respect. It's about teaching her that sometimes things that might make you feel good for a brief moment will cause you damage in the long term.
And most importantly, it's about leading by example.
Start having three healthy, balanced meals a day with no snacking in between and treat family meals as a happy, social, enjoyable thing where you all come together around the table to try new, healthy recipes. Lean proteins, vegetables, salads and healthy fats can still make for some gorgeous, creative, delicious meals that will keep her full until the next meal - there doesn't have to be refined carbs and pudding at every sitting.
In addition, start doing physical activity with her, or get her enrolled in some kind of sport, go running or cycling with her or even just take family walks. Empower her, make her start seeing her body in terms of what it can do, not in terms of what it looks like. Encourage her to push her limits.
And no, I don't think there's anything wrong with using the "f-word", as other people have said. It doesn't need to be framed in terms of "attractiveness" or body image but being overweight has real, undeniable and often fatal long term health consequences and you are absolutely right to be honest with her about this.
It probably won't be easy at first but you can definitely make positive changes now which will give her the tools for the future to make good choices, respect her body and focus on being strong and physically capable.
Good luck!